This target distribution is used as it strengthens soft cluster probabilities for each image (i.e. encourages high probabilities to become higher, and low probabilities to become lower) by putting more weight on the data points assigned to clusters with high-probability, as implemented in the equation by squaring the probability, \(q^2_{ik}\) , then normalizing by the sum of probabilities for cluster \(k\)  across all images. Additionally, it prevents large clusters from monopolizing the feature space by normalizing across the clusters, as implemented with the denominator [1]}.
